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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [32] had the largest ratio of [25]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 6 6 1.00 17 0.353
2 A 5 5 1.00 17 0.294
3 A 4 4 1.00 15 0.267
4 A 4 4 1.00 13 0.308
5 A 0 0 0.00 0 0.000
6 A 0 0 0.00 0 0.000
7 A 4 4 1.00 14 0.286
8 A 4 4 1.00 16 0.250
9 A 13 8 1.00 17 0.471
10 A 11 9 1.00 17 0.529
11 A 10 10 1.00 15 0.667
12 A 3 2 1.00 13 0.154
13 A 0 0 0.00 0 0.000
14 A 0 0 0.00 0 0.000
15 A 3 2 1.00 14 0.143
16 A 3 2 1.00 16 0.125
17 A 26 10 1.00 17 0.588
18 A 23 12 1.00 17 0.706
19 A 15 11 1.00 15 0.733
20 A 3 2 1.00 13 0.154
21 A 0 0 0.00 0 0.000
22 A 0 0 0.00 0 0.000
23 A 3 2 1.00 14 0.143
24 A 3 2 1.00 16 0.125
25 A 6 3 1.00 23 0.130
26 A 5 3 1.00 23 0.130
27 A 4 3 1.00 21 0.143
28 A 2 1 1.00 15 0.067
29 A 4 3 1.00 23 0.130
30 A 5 4 1.00 23 0.174
31 A 6 4 1.00 23 0.174
32 A 10 3 1.00 25 0.120
33 A 8 3 1.00 25 0.120
34 A 6 3 1.00 23 0.130
35 A 4 3 1.00 17 0.176
36 A 6 3 1.00 25 0.120
37 A 8 4 1.00 25 0.160
38 A 10 4 1.00 25 0.160
39 A 14 3 1.00 25 0.120
40 A 11 3 1.00 25 0.120
41 A 8 3 1.00 23 0.130
42 A 4 3 1.00 17 0.176
43 A 8 3 1.00 25 0.120
44 A 11 4 1.00 25 0.160
45 A 14 4 1.00 25 0.160
46 A 6 6 1.00 25 0.240
47 A 5 5 1.00 25 0.200
48 A 4 4 1.00 23 0.174
49 A 5 5 1.00 17 0.294
50 A 0 0 0.00 0 0.000
51 A 0 0 0.00 0 0.000
52 A 13 8 1.00 25 0.320
53 A 11 9 1.00 25 0.360
54 A 11 11 1.00 23 0.478
55 A 4 3 1.00 17 0.176
56 A 0 0 0.00 0 0.000
57 A 0 0 0.00 0 0.000
58 A 26 10 1.00 25 0.400
59 A 24 13 1.00 25 0.520
60 A 17 12 1.00 23 0.522
61 A 4 3 1.00 17 0.176
62 A 0 0 0.00 0 0.000
63 A 0 0 0.00 0 0.000
64 A 5 4 1.00 17 0.235
65 A 8 4 1.00 19 0.210
66 A 11 4 1.00 19 0.210
67 A 0 0 0.00 0 0.000
68 A 0 0 0.00 0 0.000
69 A 0 0 0.00 0 0.000
70 A 8 3 1.00 25 0.120
71 A 6 3 1.00 25 0.120
72 A 4 3 1.00 23 0.130
73 A 0 0 0.00 0 0.000
74 A 0 0 0.00 0 0.000
75 A 0 0 0.00 0 0.000
76 A 5 5 1.00 24 0.208
77 A 4 4 1.00 24 0.167
78 A 3 3 1.00 22 0.136
79 A 2 2 1.00 21 0.095
80 A 0 0 0.00 0 0.000
81 A 0 0 0.00 0 0.000
82 A 6 6 1.00 24 0.250
83 A 5 5 1.00 24 0.208
84 A 5 5 1.00 22 0.227
85 A 2 2 1.00 21 0.095
86 A 0 0 0.00 0 0.000
87 A 0 0 0.00 0 0.000
88 A 12 9 1.00 24 0.375
89 A 11 10 1.00 24 0.417
90 A 4 3 1.00 22 0.136
91 A 2 2 1.00 21 0.095
92 A 0 0 0.00 0 0.000
93 A 0 0 0.00 0 0.000

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